creators_name: Bracic, Janko,  
creators_name: Moslehian, Mohammad Sal,  
creators_id: janko.bracic@fmf.uni-lj.si
creators_id: moslehian@ferdowsi.um.ac.ir
type: article
datestamp: 2007-12-17 05:07:10
lastmod: 2008-08-16 01:45:23
metadata_visibility: show
corp_creators: University of Ljubljana, Dept. of Mathematics
corp_creators: Ferdowsi University, Dept. of Mathematics
title: On Automatic Continuity of 3-Homomorphisms on Banach Algebras
ispublished: pub
subjects: Q
full_text_status: none
keywords: 3-homomorphism, Homomorphism, Continuity, Banach algebra, Bounded approximate identity, Second dual, Arens regularity, C*-algebra.

abstract: A linear map $\varphi : \mathcal{A} \rightarrow \mathcal{B}$ between (Banach) algebras is called 3- homomorphism if $\varphi (abc) = \varphi (a)\varphi (b)\varphi (c)$ for each $a, b, c \in \mathcal{A}$. We investigate 3-homomorphisms on Banach algebras with bounded approximate identities and establish in two ways (for unital and non-unital cases) that every involution preserving homomorphism between $C^\ast$-algebras is norm decreasing.

date: 2007
date_type: published
publication: Bulletin of the Malaysian Mathematical Sciences Society
volume: 30
number: 2
publisher: Penerbit Universiti Sains Malaysia
pagerange: 195-200
refereed: TRUE
issn: 0126-6705
official_url: http://math.usm.my/bulletin/pdf/v30n2/v30n2p10.pdf
related_url_url: http://math.usm.my/bulletin/html/vol30_2_10.htm
referencetext: [1] H.G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monographs 24, Clarendon Press, Oxford, 2000.

[2] L.A. Harris, A generalization of C*-algebras, Proc. Lond. Math. Soc. 42(3)(1981), 331-361.

[3] S. Hejazian, M. Mirzavaziri and M.S. Moslehian, n-homomorphisms, Bull. Iranian Math. Soc. 31(1)(2005), 13—23.
citation: Bracic, Janko, and Moslehian, Mohammad Sal, (2007) On Automatic Continuity of 3-Homomorphisms on Banach Algebras. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 195-200. ISSN 0126-6705